The short answer to that question is yes, although it is more involved. At a public university in almost all instances, a student is allowed the right to legal representation. That being said, depending on a particular school involved, the particular charge also or process involved, at certain stages during the process, an attorney may not be able to be directly involved, although that's the exception and not the rule. At a private university, it's a more involved consideration. In most instances, an attorney is not able to be directly involved with the school unless, say, the charge involves Title IX sexual misconduct. In those instances, the expectation is that an attorney in 99.9 out of a hundred times would be allowed to be directly involved.
The student always has the right to have legal representation even if they're working, say in a behind the scenes matter, but there are exceptions in the sense of even if a school has an allowance where a legal representation is not directly allowed, there are exceptions that can be made. An experienced attorney advisor would know how to take these steps or would know how to get favorable potential discretion with the school to be involved in a capacity that may be much further than what the policy would state.